In a game about traveling, it makes sense that experience might primarily come from travel itself rather than from finding treasures or defeating monsters.
In Ryuutama, players earn a single XP award each time they finish a "leg" of their journey, based on the most difficult terrain they passed through on that part of their trip. You can earn 100-500 experience per trip, depending on the terrain and weather, plus a possible bonus for the most difficult combat, typically another 30-60. The XP totals needed to level up are comparable to 5e.
Players are encouraged to keep travelogues about their journeys, but I don't think there's a mechanical benefit to doing so. There is one other possible reward though - once per section of the trip, a Minstrel character can write a song about either the weather or the terrain, then sing it later under similar conditions to help out the other party members.
One consequence of this system is that it's more rewarding to take trips with short legs and frequent stopovers than to travel long stretches without visiting a town. It's an experience system that is well-suited to a game where you're traveling through settled lands, and where you're interested in staying awhile in each settlement. It would work less well in a campaign where you're exploring trackless wilderness, or where you pause at waystations so briefly that they're little different from any other campsite. It's also an experience system that's better suited to maps where players have some freedom to decide both where they'll travel and how they'll get there. It would work less well on map with only a single fixed route.
In Neoclassical Geek Revival, Zzarchov also awards XP directly for travel and exploration. Zzarchov's system is intended to reward and encourage longer journeys. Each session, each new room visited within a dungeon is worth more XP than the previous room - but if the players leave the dungeon, the reward resets to zero. The goal is to tempt players, perhaps against their better judgment, to press on further each delve than they might go otherwise.
"Experience points for a dungeon are granted based on how many rooms
you had previously explored for the first time in this delve. The first
new room might be worth 0xp, the second 10xp, the third an additional
30, the fourth an additional 60. This leads characters to constantly
risk defeat by wanting one more room since leaving the dungeon to rest
will reset the XP clock as it were. Trying to make it through that 13th
room (which may be empty) is worth 780xp now or 0 if they return to the
surface to rest. "
If we applied this system to overland travel, the specific unit of exploration that replaces "room" would depend on the kind of map you draw, whether hexes, grids, points, or something else. The most important thing to notice is that this system discourages the players from stopping in town. The longer they can remain out in the field, the more each discovery will be worth. This encourages an entirely different playstyle than Ryuutama's experience system.
The Dwimmermount megadungeon includes supplemental rules for earning experience (and money!) by selling maps of the dungeon and by selling clues that help answer key questions about the dungeon's history. I first learned about these mechanics from Dreams in the Lich House's review of Dwimmermount. In any game where players earn experience for finding treasure, setting our rules to assign prices to maps and clues creates a way for players to earn experience for exploration that fits within the existing framework of gp = XP.
The review suggests some basic considerations for anyone designing rules for assigning values to maps. "The book provides guidelines on the value of player maps based on the number of doors and rooms, and these scale with the depth of the dungeon level from hundreds to thousands of gold pieces in value." I suspect this works best when the players actually draw out a map. You could probably come up with a similar framework for assigning monetary values (and experience!) to player-written session reports, if you wanted to make an incentive for keeping diaries as well as for drawing maps.
One decision you would need to make would be whether to have the value of the map increase with its size in such a way that players get more for making several small maps or more for producing a single larger map. It initially seems to me more appropriate to make a single large map worth more than the sum of its smaller parts, but there is one reason to set the prices so that several small maps are worth more than the single collected version.
Players could face an interesting decision-making dilemma if selling maps creates a risk where rival adventurers might use the maps to swoop in and snatch up treasures the players hadn't collected yet. This dilemma is more severe if small maps are worth more than large ones. If the multi-session map is worth more, then there's little incentive to sell the map until after all the exploration is complete and all the treasures collected. If single-session maps are worth more, then the players will have to decide if the predictable depreciation of the map price is worth more than the potential, unpredictable loss of unclaimed treasures to rival adventurers.
Deciding on prices for clues to campaign setting mysteries seems like it might require the game master knowing what the all the mysteries and their solutions are. Without knowing those things, it might be hard to decide what counts as a clue, and when the players have accumulated enough clues to sell off their accumulated evidence.
Unlike with the maps, there doesn't seem to be any trade-off holding on to clues until you can sell a complete answer - aside from the general financial dilemma of whether you need money right now so badly that you're willing to accept less money overall to get some of it right away. My inclination is to say that complete answers should be worth quite a bit more than the individual clues that lead up to them.
The review provides a glimpse of what the maximum level of game master pre-planning and organization might look like. "Players can monetize exploration by recovering the secret history of Dwimmermount. There's a thorough discussion of the secret history, organized numerically, and these key facts can be gleaned throughout the dungeon from a range of sources. There are over 80 of them! Bringing evidence corroborating the secret history facts back to the surface allows the players to sell this information for exorbitant amounts of money when they accumulate enough facts to answer key questions about the world."
Travel and collecting clues about campaign mysteries are both types of exploration. Mapping and note-taking are both ways that players document what they've explored. Melancholies and Mirth has a guide to awarding experience for both exploration and combat. The key idea here seems to be running a campaign where the players still earn XP for treasure, but where the primary source of treasure is bringing documents and objects to interested organizations within the game world, rather than treasure hunting per say.
As with Dwimmermont, earning any of these rewards requires the players to find an NPC who wants to buy what they're selling. In Dwimmermount though, I think the conceit is that basically everyone is interested in maps and clues about the megadungeon - so the players can sell to whoever they like, and might use these sales to improve their relationship with key NPC factions. In these rules, certain organizations exist in every town, and serve more as generic quest-givers than as well-developed NPCs. There's nothing actually preventing giving those buyers names and personalities though, so if your players seem to prefer some quests more than others, it might be worth developing the NPCs on the other side of those transactions a bit more.
Melancholies and Mirths assigns prices to both dungeon maps and maps of the countryside, to secrets and pieces of history, to proof-of-death for both monsters and human NPC criminals, and to a few other things, including rare materials, presumably the type that can be used to make magic items. Again, the main difference between this and any other campaign is that most of the money and XP the players earn will come from exploration and collecting non-monetary treasures rather than from finding hordes of coins; and none of the XP rewards are automatic, but only occur after the players bring the desired objects to their respective NPC admirers.
A couple other bloggers have suggested creating rewards like this, but they've built the chance to earn additional experience into specific new character classes, rather than writing them up as opportunities that any character might participate in. I suppose this has the benefit of letting interested players portray particular archetypes (with their game master's permission, presumably) while leaving the primary game rules untouched.
One possible downside though would be if this turned into "my character gets extra treasure and levels up faster for doing the same kinds of things as everyone else". So if you did introduce rules that award XP for exploration to some characters and not others, I think you'd want to be vigilant to the possibility of conflict arising over perceptions of unfairness. (Although I haven't tried that, so I might be worrying about a possibility that doesn't arise often in practice.)
Cavegirl presents an Artist character class who can spend an hour of game time to paint "an unusual or impressive sight - which might be a strange landscape, monster, magnificent chamber in a dungeon, supernatural phenomenon, or something else". Paintings are worth 500 in cash and XP. The Artist's other abilities are pretty negligible, they're like a Thief with no thief skills, or a Wizard with no spells, so maybe leveling up really fast is fair compensation? I like the idea of roleplaying a character who's an artist, but I feel like the Artist would be a more interesting class if they were more like the Ryuutama Minstel or Goblin Punch's Bug Collector class, where the reward for identifying and studying an impressive site is to gain a new special ability that can only be acquired this way.
Monsters and Manuals suggests an Adventurer Sage class who earns money and XP for selling drawings of monsters, specimens of monsters, and of course, maps of dungeons and wilderness sites. The sizable rewards for bringing back complete monster corpses and capturing living monsters might even be enough to prompt players to approach combat differently than they usually would. This isn't far off from Melancholies and Mirth's alternate experience system, except that the Sage is the only character who benefits from it. Again, I like the idea of portraying a botanist or zoologist who's more interested in collecting natural specimens than in hunting for monetary treasure. It sounds fun. But beyond that concept, I'm not sure that being able to earn XP in an unusual way is very interesting as a character class's only special ability.
When I first saved the links to both these classes, I expected I'd be praising them, but on reflection, I think it would be better to make the cash and experience rewards for painting landscapes and studying monsters into general rules that could apply to any character. Aside from a class name that can provide a jumping off point for roleplaying a fussy aesthete or a nerdy scientist, neither the Artist or Adventurer Sage can actually do anything that other characters can't. They're like fighters with smaller Hit Dice, less armor, and lower XP requirements to gain levels.
In Final Fantasy VI, Relm is an artist who can sketch monsters and then summon magical monster drawings to fight on her behalf, Strago is a magician who can study monsters' magical abilities and then cast them as spells himself, and Gau is a feral child who can observe monsters' natural behavior and enter a rage where he imitates their physical attacks. Something like that interests me, personally, far more than class-specific experience bonuses.
So if I think that XP for exploration should be universal rather than character specific, what kinds of rewards do I think should be available to character classes that are especially exploration focused? I mentioned Ryuutama's Minstrel back at the beginning. Like most other bard-like characters, they can inspire others to do better on certain rolls, but with an added mini-game of learning songs while you travel that can only inspire under certain terrain and weather conditions. In some sense, the Minstrel is worse than other bards, since they can't sing their songs just any time, but somehow the mental challenge of deciding which songs to learn, and the emotional reward you experience when your planning pays off later seems to make up for that limitation. It's an ability that's less useful, but more fun. (It's also unlikely to ever be use-less, unlike some other "Goldilocks" abilities. You don't have to pick your songs in advance, unlike a ranger selecting their Favored Enemy or Favored Terrain, so you'll never be disappointed to discover that you can't sing Song of the Snowstorm because it turns out the campaign is actually set in the tropics.)
Goblin Punch's Bug Collector is a bit like a wizard who gets terrain-specific spells each day. Every morning before breaking camp, the Bug Collector finds a random assortment of local bugs, and can capture a certain number of them. The bugs live for 1 day in captivity, and each bug can perform a single trick, once, so mechanically this is very much like casting any other spell in D&D. But there's something kind of joyful about the presentation, and the fact that your spells are random each day, but the spell list they're drawn from is tied to the local landscape, provides a nice mix of surprise and player choice.
Pathfinder Ultimate Wilderness offers a similar ability in the Geomancer archetype for Occultists. The Geomancer can learn a set number of spells of the player's choice each level, but they also know bonus spells based on whatever kind of terrain they're currently inhabiting. These aren't chosen randomly like they for the Bug Collector, and they can change mid-day if the character passes from one terrain type to another. It still seems like it would add a fun bit of variety to the character, and would make decisions about where to travel matter in a fairly concrete way.
The Cartographer archetype for Investigators provides a mechanical reward for map-drawing that's pretty similar to the Minstrel's songwriting. Instead of inspiring others, the Cartographer can benefit themselves by studying the map they just drew of their current location. The only flaw here, ironically, is that you would never not be able to use this ability, so it lacks some of the charm of the Minstrel's matching-terrain requirement. (Potentially you could re-introduce the charming sense of limitation by only allows maps to be useful on a return visit to a previously mapped spot.) For a game master wanting to add exploration-based abilities to their game, the Cartographer and Minstrel do have one other upside. Unlike the Geomancer or the Bug Collector, this sort of simple bonus-granting ability doesn't require an extensive list of possible spell effects before you can introduce it at your table.